Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

Probing of unusual DNA structures in topologically constrained form V DNA: use of restriction enzymes as structural probe

The ability of DNA sequences to adopt unusual structures under the superhelical torsional stress has been studied. Sequences that are forced to adopt unusual conformation in topologically constrained pBR322 form V DNA (Lk=0) were mapped using restriction enzymes as probes. Restriction enzymes such as BamHI, Pstl, Aval and HindIII could not cleave their recognition sequences. The removal of topological constraint relieved this inhibition. The influence of neighbouring sequences on the ability of a given sequence to adopt unusual DNA structure, presumably left handed Z conformation, was studied through single hit analysis. Using multiple cut restriction enzymes such as Narl and Fspl, it could be shown that under identical topological strain, the extent of structural alteration is greatly influenced by the neighbouring sequences. In the light of the variety of sequences and locations that could be mapped to adopt non-6 conformation in pBR322 form V DNA, restriction enzymes appear as potential structural probes for natural DNA sequences.

Hopping and non-hopping localized ionic motion: β-AgI and β-Ag3SI

In β-AgI and β-Ag3SI the ionic conductivity has been measured at frequencies from 1kHz to 2.6 GHz and from 10 MHz to 10 THz, respectively. In both phases we observe a conductivity increase of some orders of magnitude, due to localized types of motion of the silver ions. In β-AgI the increase is found at about 1 MHz and reflects cooperative back-and-forth hopping processes between adjacent tetrahedral sites. In β-Ag3SI the phenomenon occurs at microwave frequencies. Here it is caused by a non-hopping, non-periodic localized Ag+-motion within shallow potentials.

Influence of non-geometrical factors on intracrystalline diffusion -- Role of sorbate-zeolite interactions

Molecular dynamics simulations on Xe in NaY and Ar in NaCaA zeolite are reported. Rates of cage-to-cage crossovers in the two zeolites exhibit trends which are contrary to that expected from geometrical considerations. The results suggest the important role of the sorbate-zeolite interactions in determining the molecular sieve properties of zeolites for small sized sorbates. The results are explained in terms of the barrier height for cage-to-cage crossover in the two zeolites.

Non-conservatively loaded stochastic columns

A new finite element method is developed to analyse non-conservative structures with more than one parameter behaving in a stochastic manner. As a generalization, this paper treats the subsequent non-self-adjoint random eigenvalue problem that arises when the material property values of the non-conservative structural system have stochastic fluctuations resulting from manufacturing and measurement errors. The free vibration problems of stochastic Beck's column and stochastic Leipholz column whose Young's modulus and mass density are distributed stochastically are considered. The stochastic finite element method that is developed, is implemented to arrive at a random non-self-adjoint algebraic eigenvalue problem. The stochastic characteristics of eigensolutions are derived in terms of the stochastic material property variations. Numerical examples are given. It is demonstrated that, through this formulation, the finite element discretization need not be dependent on the characteristics of stochastic processes of the fluctuations in material property value.

Growth temperature induced effects in non-polar a-plane GaN on r-plane sapphire substrate by RF-MBE

Non-polar a-plane GaN films were grown on an r-plane sapphire substrate by plasma assisted molecular beam epitaxy (PAMBE). The effect of growth temperature on structural, morphological and optical properties has been studied. The growth of non-polar a-plane (1 1 - 2 0) orientation of the GaN epilayers were confirmed by high resolution X-ray diffraction (HRXRD) study. The X-ray rocking curve (XRC) full width at half maximum of the (1 1 - 2 0) reflection shows in-plane anisotropic behavior and found to decrease with increase in growth temperature. The atomic force micrograph (AFM) shows island-like growth for the film grown at a lower temperature. Surface roughness has been decreased with increase in growth temperature. Room temperature photoluminescence shows near band edge emission at 3.434-3.442 eV. The film grown at 800 degrees C shows emission at 2.2 eV, which is attributed to yellow luminescence along with near band edge emission. (C) 2010 Elsevier B.V. All rights reserved.

5-Fluorouracil induces structural changes in rat liver tRNA

5-fluorouracil (FUra) has been shown to modulate the aminoacylation function of rat liver tRNA. The present study was aimed at studying the structure-function relationship of FUra-substituted tRNA. Male Wistar rats (2-3 month old) were given a single i.p. injection of FUra at 50, 250, or 500 mg/kg body wt. and FUra-substituted total liver tRNA, i.e. tRNA(FUra50, 250, and 500, respectively, were isolated 3 h later. Normal tRNA (tRNA(N)) was isolated from saline-treated control rats. Thermal denaturation studies showed higher melting temperatures for tRNA(FUra) compared to tRNA(N). Heat denaturation followed by renaturation of total tRNA did not affect the activity of tRNA(N) and tRNA(FUra50), where as tRNA(FUra250 and 500) lost 35% and 72% of activity, respectively, compared to the corresponding group of non-denatured tRNA. Antibodies specific to rat liver tRNA recognized normal and FUra-substituted tRNA in the order of tRNA(N) > tRNA(FUra50) > or = tRNA(FUra250) > tRNA(FUra500) in an avidin-biotin micro-enzyme linked immunosorbant assay. tRNA(N) or tRNA(FUra50) preincubated with tRNA antiserum showed 74% and 59% of aminoacylation activity, respectively, compared to that of corresponding tRNA preincubated with normal rabbit IgG. However, activities of similarly treated tRNA(FUra250 and 500) were not affected. The observations of possible changes in the secondary structure of rat liver tRNA upon incorporation of FUra are discussed.

A structural study of Li2S---B2S3 glasses by neutron diffraction

The radial distribution functions (RDFs) of five xLi2S.(1 - x)B2S3 glasses (x = 0.55, 0.60, 0.67, 0.71 and 0.75) have been determined from neutron diffraction experiments performed at the Institut Laue-Langevin, Grenoble. These glasses are prepared by casting a molten mixture of boron, sulphur and Li2S inside a controlled atmosphere glovebox. Addition of the Li2S Modifier is found gradually to suppress all peaks corresponding to interatomic distances > 3.5 angstrom, which implies that the structural entities present in these glasses become segmented, and therefore more ionic, as x increases. The assumption of the existence of four main structural entities based on four- and three-coordinated borons (the latter carrying bridging and/or non-bridging sulphurs) accounts for all the peaks present in the RDFs as a function of composition. Furthermore, in the most modified glass (x = 0.75), that which contains only 'isolated' BS33- triangles, there seems to be evidence for either octahedral or tetrahedral coordination of Li+ by S- ions

Ebselen is a potent non-competitive inhibitor of extracellular nucleoside diphosphokinase

Nucleoside di- and triphosphates and adenosine regulate several components of the mucocilairy clearance process (MCC) that protects the lung against infections, via activation of epithelial purinergic receptors. However, assessing the contribution of individual nucleotides to MCC functions remains difficult due to the complexity of the mechanisms of nucleotide release and metabolism. Enzymatic activities involved in the metabolism of extracellular nucleotides include ecto-ATPases and secreted nucleoside diphosphokinase (NDPK) and adenyl kinase, but potent and selective inhibitors of these activities are sparse. In the present study, we discovered that ebselen markedly reduced NDPK activity while having negligible effect on ecto-ATPase and adenyl kinase activities. Addition of radiotracer gamma P-32]ATP to human bronchial epithelial (HBE) cells resulted in rapid and robust accumulation of P-32]-inorganic phosphate ((32)Pi). Inclusion of UDP in the incubation medium resulted in conversion of gamma P-32]ATP to P-32]UTP, while inclusion of AMP resulted in conversion of gamma P-32]ATP to P-32]ADP. Ebselen markedly reduced P-32]UTP formation but displayed negligible effect on (32)Pi or P-32]ADP accumulations. Incubation of HBE cells with unlabeled UTP and ADP resulted in robust ebselen-sensitive formation of ATP (IC50=6.9 +/- 2 mu M). This NDPK activity was largely recovered in HBE cell secretions and supernatants from lung epithelial A549 cells. Kinetic analysis of NDPK activity indicated that ebselen reduced the V-max of the reaction (K-i=7.6 +/- 3 mu M), having negligible effect on KM values. Our study demonstrates that ebselen is a potent noncompetitive inhibitor of extracellular NDPK.

Effects of halogen substitution in nucleic acid components. Structure of sodium 5-bromocytidine 5'-phosphate hydrate

The conformation of 5-bromocytidine 5'-monophosphate in the title compound, Na+.C9H11BrN3O8P-.1.25H2O, is anti, C(3')-endo and gauche-gauche, similar to that in analogous non-halogenated nucleosides/nucleotides. The Na ion coordinates directly with phosphate O atoms and base atoms. Br is not involved in any stacking interaction.

Non-Fermi liquid behavior in a mean-field study of the t-J model: Role of zero-point spin fluctuations

We present analytic results to show that the Schwinger-boson hole-fermion mean-field state exhibits non-Fermi liquid behavior due to spin-charge separation. The physical electron Green's function consists of three additive components. (a) A Fermi-liquid component associated with the bose condensate. (b) A non-Fermi liquid component which has a logarithmic peak and a long tail that gives rise to a linear density of states that is symmetric about the Fermi level and a momentum distribution function with a logarithmic discontinuity at the Fermi surface. (c) A second non-Fermi liquid component associated with the thermal bosons which leads to a constant density of states. It is shown that zero-point fluctuations associated with the spin-degrees of freedom are responsible for the logarithmic instabilities and the restoration of particle-hole symmetry close to the Fermi surface.

Soft-chemical synthesis of new non-linear optical materials, K0.5M0.5Ti0.5OPO4(M = Nb, Ta),related to KTiOPO4

Soft-chemical oxidation of KTiOPO4-like KM(0.5)(V)Ti(0.5)(III)OPO(4) (M = Nb, Ta) using chlorine in CHCl3 is accompanied by partial deintercalation of potassium, yielding K(0.5)MV(0.5)Ti(0.5)(IV)OPO(4) compounds which are new non-linear optical materials that exhibit efficient second-harmonic generation of 1064 nm radiation, as does KTiOPO4.

Surface barrier effects in non-resonant microwave absorption by superconducting thin films of YBa2Cu3O7??

We present an unusual temperature dependence of hysteresis in the Lion resonant microwave absorption (NRMA) signals from superconducting thin films of YBa2Cu3O7-delta. We observe that the hysteresis increases with increase in temperature till T-c which we interpret as evidence for the presence of Bean-Livingston surface barriers (BLSB) in the single crystalline films.